Question

Prove that the complement of the Cantor set is an open set

Answer #1

Prove the following in the plane.
a.) The complement of a closed set is open.
b.) The complement of an open set is closed.

Prove by contradiction that "The Cantor Set is Uncountable"

Prove there exists an onto (and 1-1) mapping from Cantor Set to
[0,1].

2. The Cantor set C can also be described in terms of ternary
expansions.
(a.) Prove that F : C → [0, 1] is surjective, that is, for every
y ∈ [0, 1] there exists
x ∈ C such that F(x) = y.

show the limit as x goes to c of the characteristic function of the
Cantor set =0 when c is not in the Cantor set and the limit does
not exist when c is in the Cantor set

Prove the Complement of Difference Lemma: ( A − B )' = A' ∪ B
using ONLY the set identities in the topical
notes.

Prove the First Complementarity Theorem: Suppose S is a point
set. Let Sc be the complement of S.
1) S and Sc have the same boundary.
2) The interior of S is the same as the exterior of Sc.
3) The exterior of S is the same as the interior of Sc.

How to prove below?
If A is an open set and f is differentiable at Xo which is
included at A, the Df(Xo) is unique.

Prove or disprove:
If A and B are subsets of a universal set U such that A is not a
subset of B and B is not a subset of A, then A complement is not a
subset of B complement and B complement is not a subset of A
complement

Use the Cantor-Schr oder-Bernstein theorem to prove that (0, ∞)
and R have the same cardinality

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